Question

In: Advanced Math

1. A surveyor is measuring a field that is in the shape of a triangle. She...

1. A surveyor is measuring a field that is in the shape of a triangle. She labels the triangle TRG. She determines the measure of angle T to be 35 degrees and the measure of angle R to be 68 degrees. She has also determined that side TR is 173.2 m long. Find the perimeter of the field to the nearest tenth of a metre. Include a sketch with your solution.

[5 point] 1. Two airplanes leave an airport, travelling in the same direction. Thirty minutes later, an observer on the ground sees the first plane with an angle of elevation measuring 64 degrees and an altitude of 9000 m. At the same time, the second plane has an angle of elevation of 36 degrees (in the opposite direction) and an altitude of 10 000 m. Find the air distance between the two planes, rounded to the nearest kilometre. Include a sketch with your solution.

Expert Solution

Solution:

1. Here in this problem the field is in the shape of a triangle.

Given that the triangle is TRG and the length of TR = 173.2 m and = 35⁰ and = 68⁰.

We have to find the Perimeter of the triangle TRG.

Let us denote the sides of the triangle as t, r and g opposite to the angles respectively. Then the perimeter P = t + r + g

We know that the total angles in a triangle sum upto 180⁰.

Therefore = 180 - = 180 - 68 - 35 = 77⁰

Now given g = 173.2 m. We need to find r and g.

We know that

Let us take the given side TR (=g) and the known angle to calculate r (=TG)

===>

Similarly

===>

Knowing the length of the sides TR (=g), TG (=r) and GR (=t), the Perimeter of TRG = t + g + r

= 102.0 + 164.8 +173.2 = 440 m

2. solution for the Aeroplane problem

In the above picture O is the observer, P1 is the plane 1 and P2 is the plane 2.

We need to find the length of P1P2.

Given data: = 64⁰, BP1 = 9000m, = 36⁰ AP2 = 10000m

We know that the sum of the angles in a triangle is 180⁰.

Therefore . Also given BP1 = 9000m.

As per the first part of the problem OB (=p1) can be found using the formula

==>

Similarly, OA can be found as follows:

and AP2 = 10000m

Now

==>

Therefore the Total distance between the two planes are

As We want the answer to the nearest Km,

Colby Messinger answered 1 year ago

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